Wickham et al. (2025) The Estimation of Evapotranspiration Rates from Urban Green Infrastructure Using the Three-Temperatures Method

Identification

• Journal: Hydrology
• Year: 2025
• Date: 2025-11-27
• Authors: Bruce Wickham, Simon De-Ville, Virginia Stovin
• DOI: 10.3390/hydrology12120315

Research Groups

• School of Mechanical, Aerospace, and Civil Engineering, The University of Sheffield, Sheffield S1 4DT, UK
• Department of Civil & Environmental Engineering, University of Liverpool, Liverpool L69 3GH, UK

Short Summary

This study evaluated the Three-Temperatures (3T) method for estimating evapotranspiration (ET) from urban green infrastructure using a plastic imitation surface, finding that while 3T-ET estimates tracked reference ET well, they consistently overestimated values and were limited to mid-morning to late afternoon due to temperature convergence issues.

Objective

• To determine whether reasonable evapotranspiration (ET) estimates can be achieved using the Three-Temperatures (3T) method with a plastic imitation surface for a small, homogenous vegetated surface analogous to sustainable drainage systems (SuDS) and/or green infrastructure (GI).

Study Configuration

• Spatial Scale: Experimental setup on a third-floor roof terrace (elevation 95 m above ordnance datum) in Sheffield, UK (53.381693°N; 1.477279°W). Two test beds: a 4 m² (2 m × 2 m) net radiation test bed and a 1 m² (1 m × 1 m) imitation surface test bed. The imitation surface was 0.0625 m² (0.250 m × 0.250 m). Grass vegetation was maintained at approximately 0.120 m height. Instruments were initially installed 0.600 m, then 0.260 m, above the test bed surface.
• Temporal Scale: Data collected at a one-minute timestep between October and November 2023 and from January to March 2024. Hourly timesteps were used for 3T-ET estimates and comparisons, providing one of the longest continuous ET estimates (112 days) using the 3T approach in an urban environment to date.

Methodology and Data

• Models used:
  • Three-Temperatures (3T) method (Qiu et al., 1996) for latent heat flux density (QLE,veg).
  • Penman–Monteith (PM) FAO-56 equation for reference evapotranspiration (ETo).
  • Equations for net shortwave radiation (QRn,sw), net longwave radiation (QRn,lw), and total net radiation (QRn) using fixed albedo (α = 0.230) and emissivity (ϵ = 0.900) values.
  • Latent heat of vaporisation (λ) calculated based on air temperature.
  • Soil heat flux density (QSoil) estimated as a fraction of net radiation (0.1 for QRn ≥ 0, 0.5 for QRn < 0).
• Data sources:
  • In-situ sensors: Net radiometers (Kipp & Zonen CNR4-L4, Apogee Instruments SN-500-SS), infrared radiometers (Apogee Instruments Sl-111-SS) for vegetated (Tveg) and imitation (Timt) surface temperatures, shielded air temperature (Tair) and relative humidity (RH) sensor (Campbell Scientific CS215), and three-cup wind anemometer (Vector Instruments A100LK).
  • External data: Daily rainfall depths from the Environment Agency’s online 15 min timestep rainfall records database (nearest station 5.60 km southwest of the study site).

Main Results

• All four 3T-ET approaches (ET1-ET4) tracked the dynamics of reference ETo reasonably well, showing good correlation (R² > 0.659).
• 3T-ET estimates consistently overestimated ET relative to ETo, with a mean absolute error (MAE) ranging from 0.05 to 0.15 mm·h⁻¹ and a percentage bias (PBIAS) from 24.4% to 81.1%.
• The 3T method is highly sensitive to changes in imitation surface temperature (Timt) and air temperature (Tair), particularly when their values converge, leading to unrealistic ET estimates. This limits the method's reliable application to between mid-morning and late afternoon.
• Filtering data to exclude night-time, building shadows, and periods of extreme temperature fraction significantly improved the accuracy of 3T-ET estimates.
• Methods incorporating measured net radiation (ET3) and soil heat flux density (ET4) produced estimates closer to ETo. ET4, which included soil heat flux, showed the lowest MAE (0.03 mm·h⁻¹ in March), suggesting that soil heat flux should not be ignored at hourly timesteps.
• The study successfully captured complex urban microclimate dynamics, including cloud cover, building shadows, and reflections, at a one-minute timestep.

Contributions

• Provided one of the longest continuous records (112 days) of 3T-ET estimates in an urban environment using a robust plastic artificial grass imitation surface, addressing limitations of previous short-term studies and paper-based imitation surfaces.
• Systematically evaluated the sensitivity of the 3T method to key parameters, clearly identifying its operational limitations to specific diurnal periods (mid-morning to late afternoon) due to temperature convergence.
• Demonstrated that incorporating measured net radiation and, crucially, soil heat flux density significantly improves the accuracy of hourly 3T-ET estimates in urban settings.
• Highlighted the potential for local microclimate effects in small urban green infrastructure footprints to cause actual ET to deviate from reference ET, suggesting the need for a location-specific factor (Kl).

Funding

• Engineering and Physical Sciences Research Council (EPSRC) DTP, grant number EP/W524360/1; project number: 2779460.

Citation

@article{Wickham2025Estimation,
  author = {Wickham, Bruce and De-Ville, Simon and Stovin, Virginia},
  title = {The Estimation of Evapotranspiration Rates from Urban Green Infrastructure Using the Three-Temperatures Method},
  journal = {Hydrology},
  year = {2025},
  doi = {10.3390/hydrology12120315},
  url = {https://doi.org/10.3390/hydrology12120315}
}